Question

已知：如圖AE⊥BC，∠EAC=∠ACD，試說明BC垂直于DC．                       

                                                                        

Answer 1

【考點】平行線的判定與性質；垂線．                                                    

【分析】利用平行線的判定推出AE∥CD，再根據平行線的性質及垂線定義可得出．                 

【解答】解：∵AE⊥BC，                                                                       

∴∠AEB=90°，                                                                                  

∵∠EAC=∠ACD，                                                                            

∴AE∥CD，                                                                                      

∴∠DCB=∠AEB=90°，                                                                           

∴BC⊥DC．                                                                                      

【點評】本題考查了平行線的判定和性質，垂直的定義，熟練掌握平行線的判定定理是解題的關鍵．